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Pierre Welander

Abstract

Stationary and transient states of a two-layer fjord-type estuary are discussed analytically. The forcing functions are the outer salinity S 0, the fresh-water supply q f, and a meteorologically forced barotropic transport q m. Forced nonlinear, time-dependent cases have been studied numerically. Some associated laboratory experiments are described.

The main results obtained are as follows: (i) A single steady state exists; this is approached in an exponential-like way. (ii) The total mixing through the interface must vary with depth (decrease for increasing interface depth) to allow a stable steady state. (iii) The static stability increases with increasing fresh-water supply, up to a critical value where the two-layer model breaks down. (iv) An added oscillatory component in S 0 increases and in q f decreases the esturay salinity and the static stability. The effect of an oscillatory q m may go in either direction. (v) The statistical steady state is sensitive to certain high-order statistical features of the forcing functions. It is suggested that changes in such statistical features, rather than changes in mean forcing conditions, may explain observed physical-chemical secular variations in the Baltic, in particular the drop of oxygen concentrations of the deep water.

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Pierre Welander

Abstract

Rossby's (1936) wake stream theory of the Gulf Stream is revived and generalized. Including the β-effect, the volume transport of the Stream should increase faster than predicted by the Tollmien-Rossby formula, in agreement with observations. The idea that the Gulf Stream is forced by the pressure head in the Florida Straits, with the wind-stress curl at the higher latitude playing a secondary role, finds some support from observations.

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Pierre Welander

Abstract

A special three-dimensional solution of similarity type is given for a meridionally closed ocean with dynamic according to Stommel's classical transport model, and with the density determined by three-dimensional advection and vertical diffusion. The boundary current exhibits a rapidly varying scale depth; this depth becomes zero at a critical latitude where the current must separate. The solution requires an upwelling everywhere, to be balanced by abyssal sources of water and a deep circulation, as described by Stommel and Arons. It is proposed that a more general similarity form may be useful in future analytical as well as numerical studies of the ocean circulation.

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Pierre Welander

Abstract

A three-dimensional regime with a differentially heated mixed layer on top of an ideal fluid interior is considered in a situation which corresponds to the interior of the well-known wind-driven model by Stommel (1948). Although the transport field in this case is continuous and simple, the same is not necessarily true for the density and velocity fields: if the mixed layer is weakly coupled to the atmosphere a front is generated at the line of a maximum downwelling; another front is expected at the line of a zero downwelling.

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Pierre Welander

Abstract

A continuously stratified inertial boundary current in a β-plane possesses a similarity solution for the pressure of the formwhere A 0(y), k 0(y), z 0(y) are arbitrary functions, n is an arbitrary constant. It can satisfy the condition u = 0 at x = 0, and be matched to a known interior solution (the thermocline solution of the power law type) but does not generally satisfy the condition w = 0 at z = 0.

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Pierre Welander

Abstract

The pressure along a closed hydrographic section can be correctly calculated from density data, in the ideal case of perfectly steady, geostrophic, density-conserving flow; and from dense, error-free data, excluding certain degenerate cues. A corresponding practical method, aimed at an estimate of the pressure from real hydrographic data, has been designed.

The calculation is made by a minimization of the volume enclosed by the surface B = F(ro,P) in the P-ro-B space, where ro is the density. P = froz the potential vorticity, and B = B* + p 0 the Bernoulli function, split in a known baroclinic part B* and an unknown pressure p 0, defined at a chosen depth z 0. The minimization is made under free variation of p 0(s), as a function of the tangential coordinate s, the minimum volume is zero under the ideal conditions. Practically, one minimizes a moment rather than the volume, with identical results in the ideal case.

The minimization requires an identification of “corresponding points” (endpoints of the same streamline) from the P-conservation; this may become impractical in the presence of strong noise. In such cases an alternative method based on an integral equation expressing the detailed flux balance of P and B is proposed.

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Pierre Welander

Abstract

The hypothesis of a zonally uniform regime for the interior oceanic circulation is advanced. The regime is found theoretically in frictional models, such as the one by Stommel (1948), when the meridional scale is small compared to the zonal one. While the interior solution is independent of longitude, there remains an east-west asymmetry of the meridional boundary currents. A discussion of more general, zonally uniform regimes in the oceans is given, and a comparison is made with the corresponding regime in the atmosphere.

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Pierre Welander and Cho-Teng Liu

Abstract

In a uniform-depth ocean forced by a wind stress and surface heat flux (or surface temperature) which are independent of longitude, there exists a possible thermocline regime with vanishing east-west temperature gradient. The associated meridional-vertical circulation is entirely wind-driven, producing a deep thermal structure at high latitudes, a thin equatorial thermocline, and a vertical thermal front at the latitude of vanishing Ekman downwelling. Some numerical examples are given.

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